Leasing an Oil Well. Assume that the price for oil (in pounds per barrel) evolves according to the following binomial lattice model. 0 100 1 2 3 110 121 133.1 90 99 108.9 81 89.1 72.9 Shown are the prices in n years from now, where n=0,1,2,3. From any non-terminal cell in the lattice we can either move to the right (by a single cell) with probability p=0.4. Or we can move to the right and down (by a single cell) with probability 1-p=0.6. Consider an oil well that produces at most 1,000,000 barrels per year. The production of oil costs 95 per barrel. We assume that oil extracted from the well in a given year is sold at the price at the beginning of the year, but the corresponding cash flow occurs at the end of the year. Moreover, we assume that the yearly interest rate is constant at 5%. What is the fair value of a 2 year lease of the oil well? Suppose that it is possible to enhance the productivity of the oil well to 2,000,000 barrels per year. This enhancement would cost 3,000,000, and it would increase the production costs to 100 per barrel. This enhancement can be installed at the beginning of any year, and once in place it applies to all future years. The enhancement becomes the property of the oil well's original owner at the end of the lease. What is the fair value of the lease in the presence of this enhancement option? Leasing an Oil Well. Assume that the price for oil (in pounds per barrel) evolves according to the following binomial lattice model. 0 100 1 2 3 110 121 133.1 90 99 108.9 81 89.1 72.9 Shown are the prices in n years from now, where n=0,1,2,3. From any non-terminal cell in the lattice we can either move to the right (by a single cell) with probability p=0.4. Or we can move to the right and down (by a single cell) with probability 1-p=0.6. Consider an oil well that produces at most 1,000,000 barrels per year. The production of oil costs 95 per barrel. We assume that oil extracted from the well in a given year is sold at the price at the beginning of the year, but the corresponding cash flow occurs at the end of the year. Moreover, we assume that the yearly interest rate is constant at 5%. What is the fair value of a 2 year lease of the oil well? Suppose that it is possible to enhance the productivity of the oil well to 2,000,000 barrels per year. This enhancement would cost 3,000,000, and it would increase the production costs to 100 per barrel. This enhancement can be installed at the beginning of any year, and once in place it applies to all future years. The enhancement becomes the property of the oil well's original owner at the end of the lease. What is the fair value of the lease in the presence of this enhancement option